Let (X) be a (operatorname{UnIform}(alpha, beta)) random variable. a. Prove that the moment generating function of (X)

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Let $X$ be a $\operatorname{UnIform}(\alpha, \beta)$ random variable.

a. Prove that the moment generating function of $X$ is $[t(\beta-\alpha)]^{-1}[\exp (t \beta)-$ $\exp (t \alpha)]$.

b. Prove that the characteristic function of $X$ is $[i t(\beta-\alpha)]^{-1}[\exp (i t \beta)-$ $\exp (i t \alpha)]$.

c. Using the moment generating function, derive the first three moments of $X$. Repeat the process using the characteristic function.

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 02:01 AM

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Let (X) be a (operatorname{UnIform}(alpha, beta)) random variable. a. Prove that the moment generating function of (X)

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Introduction To Statistical Limit Theory

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